When someone sends mail to firstname.lastname@example.org, their email program either connects directly to yourdomain.com, or it passes it off to somebody else’s mail server which then connects directly to yourdomain.com. If Your machine is yourdomain.com, it gets there right then. But if yourdomain.com is hosted by someone else, yes, it gets There immediately but that doesn’t mean that you can get it.
Consider your typical large ISP like GMAIL. How many email messages do you think land at GMAIL’s servers every second? An unimaginable number. Computers are fast, but they can only do what they can do: GMAIL may take minutes or sometimes even hours before it can process your mail and put it somewhere where you can get it.